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Exercises for Question Type 2: Finding the FOC for functions using technology - IB | RevisionDojo

Question 1

Calculus: Differentiation and finding stationary points of polynomial functions.

Find the stationary points of $f(x) = x^5 - 5x + 3$ .

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Question 2

Find the derivative of $f(x) = \sin x + x$ and identify the stationary point(s) in the interval $[0, 2\pi]$ .

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Question 3

Determine the $x$ -coordinates of the stationary points of $f(x) = \frac{x^2 e^x}{x - 1}, x \neq 1$ .

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Question 4

Find the first order condition (FOC) for the function $f(x) = \frac{e^x}{x - 1}$ and determine its stationary point.

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Question 5

The question requires students to differentiate a polynomial function, solve for the roots of the derivative to find stationary points, and determine the corresponding coordinates.

Determine all stationary points of $f(x) = x^4 - 4x^3 + 6x^2 - 4x + 1$ .

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Question 6

Determine the first-order condition for $f(x) = x e^x$ and find its stationary point.

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Question 7

Determine the first derivative of $f(x) = \displaystyle\frac{\ln x}{x}$ , $x > 0$ , and find the coordinates of the stationary point.

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Question 8

Find the stationary points of $f(x)=x^2\sin x$ on $[0,\pi]$ .

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Question 9

Determine the first-order conditions for $f(x) = x^3 - 3x^2 + 2$ and find all stationary points.

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Question 10

Find the stationary point of $f(x) = x \ln x - x$ for $x > 0$ .

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Question 11

Find the stationary point of the function $f(x)=3x^2+2x-5$ .

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Question 12

This question requires the application of the chain rule to find the derivative of a logarithmic function and determining the coordinates of its stationary point.

Find the stationary points of $f(x) = \ln(x^2 + 1)$ .

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Question Type 2: Finding the FOC for functions using technology Exercises