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(a) (i) Find the equation of the tangent to the graph of f(x) = e² at x = 0. (ii) Show that the function f(x) = eª is convex. (iii) Using parts (i) and (ii), explain why e 2x+1, for all z E R.

(a) (i) Find the equation of the tangent to the graph of f(x) = e² at x = 0. (ii) Show that the function f(x) = eª is convex. (iii) Using parts (i) and (ii), explain why e 2x+1, for all z E R.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter6: Applications Of The Derivative
Section6.3: Implicit Differentiation
Problem 26E
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(a) (i) Find the equation of the tangent to the graph of f(x) = e² at x = 0.1 (ii) Show that the function f(x) = eª is convex. (iii) Using parts (i) and (ii), explain why e 2+1, for all a € R. (b) Find the integers n in the interval (0, 10) such that the function g(x) = cos() has a stationary point at x = ².
Transcribed Image Text:(a) (i) Find the equation of the tangent to the graph of f(x) = e² at x = 0.1 (ii) Show that the function f(x) = eª is convex. (iii) Using parts (i) and (ii), explain why e 2+1, for all a € R. (b) Find the integers n in the interval (0, 10) such that the function g(x) = cos() has a stationary point at x = ².
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