Exercises for Question Type 2: Determining whether points satisfying the first order condition are local optimals - IB | RevisionDojo

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Question Type 2: Determining whether points satisfying the first order condition are local optimals

Question Type 2: Determining whether points satisfying the first order condition are local optimals Exercises

Question 1

Determine the stationary points of $f(x)=x^2e^{-x^2}$ and classify each.

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Question 2

Find and classify the stationary points of the function $f(x) = x^3 e^{-x}$ .

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Question 3

Determine the stationary points of $f(x) = \frac{x^2e^x}{x-1}$ for $x \neq 1$ and state their nature (minimum or maximum).

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Question 4

Find the stationary point of $f(x) = e^{-x}(x + 2)$ and state its nature.

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Question 5

Determine the stationary point(s) of the function $f(x) = \frac{e^x}{x + 1}$ and state whether each is a minimum or maximum.

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Question 6

Determine the stationary point(s) of $f(x)=e^x(x-1)^2$ and state their nature.

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Question 7

Stationary points and their classification using the first derivative test.

Determine and classify the stationary points of $f(x)=\frac{x^2}{e^x}$ .

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Question 8

Stationary points and their classification for a function involving an exponential term.

Find and classify the stationary points of the function $f(x) = (x - 2)^2 e^{-x}$ .

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Question 9

Find the stationary points of $f(x) = \frac{e^x}{x^2-3}$ and determine their nature.

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Question 10

Calculus: Stationary Points

Find the stationary points of the function $f(x) = x^2e^x$ and determine whether each is a local minimum or maximum.

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Question 11

Determine the stationary point of the function $f(x) = x e^{-x}$ and state its nature.

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Question 12

Find the stationary points of $f(x) = xe^{-x}$ and classify them.

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