Sketch the graph of a function that satisfies all of the following conditions. f'(0) = f'(4) = 0 f'(x) > 0 if 0 < x < 4, and f'(x) < 0 if x < 0 or x > 4 f"(x) > 0 if x < 2 and f"(x) < 0 if x > 2

Q: h(x)=(x° +1} (2x+5)*

A: Given : hx = x2+132x+52

Q: Find the derivative of the function. Simplify where possible. f(x)   = x In(arctan x)

A: Given: The above function contains two functions, so the product rule is used to differentiate.

Q: Find the derivative of the function by the limit process. f(x)= 2/x2

A:

Q: Find the derivative of arctan(x² + 1) -2x O f' (x) = -2a2 – a4 2x f' (æ) = x² +2 2x f' (x) x4+2x²+2…

A:

Q: Find the derivative of the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

Q: Consider the function f(x)  whose second derivative is f"(x) = 10x+4sin(x) . If f(0)=2  and f'(0)=3…

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Q: Find the derivative of the function by the limit process. f(x) = 6/x

A: Given fx=6xddxfx=limh→0fx+h-fxh

Q: Use central difference method to estimate the 1st derivative of the following function at x = 2 and…

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Q: find the function with the given derivative whosegraph passes through the point P. ƒ'(x) = 2x - 1,…

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Q: f(x)= xe* In(x³)

A: f(x)=xe-xln(x3)According to question we have to calculate the derivative of the function.

Q: Find the derivative of f(x) = 1 at x = 3

A: The given function is: fx=1x Using the formula of derivative i.e., ddxxn=nxn-1

Q: Find the derivative of the function by the limit process. f(x) = √(x + 4)

A: Given function is

Q: apply 1rt and second derivative to sketch graph  1)f(x)=3+7e^(-0.2x) and  2)f(x)=ln(2x+4)

A: In the question we have to draw the graph.

Q: Suppose the derivative of the function y = f(x) is y' = (x- 2) (x + 6). At what points, if any, does…

A: see 2nd step

Q: 1 Find the first derivative given that f(x) = xdx +

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Q: Suppose that the SECOND DERIVATIVE of a function f is given by f" (x) = (x – 2)² (x² – 4x). Find the…

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Q: Solve the first derivative of f(x) = 52x+1 at x = 0.5 using backward finite-divided difference and a…

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Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: 2) Find the derivative of the function f(x) = (x³ – tan(4x² – 2)* |

A: Given :            To find the derivative of the given function                f(x) = x3 -…

Q: Find all possible functions f with the given derivative. f'(x)= 1/x-1, x is greater than 1

A: Obtain the all possible functions as follows.

Q: Find the most general anti-derivative of f(x) = 9Vx +1+ cos x.

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Q: Find the derivative of the function by the limit process.

A: The given function is fx=-5x. Obtain the derivative as follows.

Q: Find the derivative of the function by the limit process.

A: Consider the function, fx=12 The limit definition of the derivatives of a function is given by the…

Q: Find an equation of the tangent line to the graph of f at the given point.

A: The equation of the tangent line to the graph of f at a given point x0,y0 is y-y0=f'(x0,y0)x-x0…

Q: find derivative of the U function 1-x f(x) = sec-1. 1+ x ーオ

A: Explanation of the answer is as follows

Q: Suppose that the second derivative of the function y = f(x) is y" = x*(x = 2)°(x + 3). For what…

A: Given: The second derivative of the function y=f(x) is y"=x2(x-2)3(x+3) Definition: The inflection…

Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Find the derivative of the function.

A: Consider the given function as y=xtan-12x-14ln1+4x2

Q: 2. Determine the second derivative of f(x) = x²e²* at x = -2 with a step-size of h=0.50 using…

A: Given function f(x)=x2e2x. The objective is to determine the second derivative of fx at x=-2 with a…

Q: Suppose that the second derivative of the function y = ƒ(x) is y′′ = (x + 1)(x - 2). For what…

A: For inflection point we must have y" = 0

Q: Find the Equation of tangent line of the function f(x) = 1+ csc(x) – cos(x) 2n 4+v3 3' 23 At the…

A: Answer

Q: Find the derivative of the function by the limit process. f(x) = 1/x2

A: Here the given function The first derivative of function f(x) is defined by limit prosses as

Q: find the derivative of f (x) at the designated value of x. f (x) = x5 at x = 3/2

A: Given function is: fx=x5 We have to find the derivative of f(x) at x=32. Then we get,…

Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: 1. Use the limit definition of the derivative to determine the derivative.2. Determine the equation…

A: We have to find derivative using limit definition of derivative and then find tangent line to f(x)…

Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function…

A:

Q: Find the derivative of the function by the limit process. f(x) = vX +7

A: Given,          The function is fx=x+7.

Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 3

A:

Q: Solve for the derivative of the function using chain rule. 8. f(x)= sin (2x)cos (3x)

A: Given problem:- Solve for the derivative of the function using chain rule.   8.     f(x)= sin…

Q: Find the derivative of f(x) = arctan x In(6x? + 6x – 4) 1 1 -In(бx? + бх — 4) + arctan x- -(12x + 6)…

A: Product rule (u v )' = u ' v + u v' Formula derivative of xn=n xn-1 Derivative of arctan…

Q: Find the equation of the tangent line to the function f(x) = x² – 2 at the point (1,-1). You must e…

A: Given, fx = x4 -2  We have to find the equation of the tangent line to function at the point 1, -1.

Q: Find the derivative of the function by the limit process. f(x) = 7

A: The given function f(x)=7. The derivative of the limit  for the function f(x) is defined by So, to…

Q: Find the derivative of the function by the limit process. f(x)=x2+x-1

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Q: Find the derivative of the function by the limit process. f(x) = 31 f'(x) =

A: The given function is fx=31.

Q: Find the derivative of the function. 5/1 x+1 In 22 + arctan x %3D X -1· dy dx

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Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

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Q: Obtain the first derivative of the function f (x) = sinx/x using Richardson's extrapolation with h =…

A: Given  f(x) = sinxx we have to obtained the first derivative of f(x) by using  Richardson's…

Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2).…

A: