Questions: Given the function f and point a below, complete parts (a)-(c). f(x)=5 x^2, x ≥ 0, a=2 f'(x)=√5 b. Graph f and f^(-1) together. Choose the correct graph below. A. B. C. D.

Given the function f and point a below, complete parts (a)-(c). f(x)=5 x^2, x ≥ 0, a=2 f'(x)=√5 b. Graph f and f^(-1) together. Choose the correct graph below. A. B. C. D.
Transcript text: Given the function $f$ and point a below, complete parts (a)-(c). \[ f(x)=5 x^{2}, x \geq 0, a=2 \] $f^{\prime}(x)=\sqrt{5}$ b. Graph $f$ and $f^{-1}$ together. Choose the correct graph below. A. $B$. C. D.
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Solution

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Solution Steps

Step 1: Identify the function and point

The given function is \( f(x) = 5x^2 \) for \( x \geq 0 \), and the point is \( a = 2 \).

Step 2: Calculate the derivative of the function

The derivative of \( f(x) = 5x^2 \) is found using the power rule: \[ f'(x) = \frac{d}{dx}(5x^2) = 10x \]

Step 3: Evaluate the derivative at the given point

Substitute \( x = 2 \) into the derivative: \[ f'(2) = 10(2) = 20 \]

Final Answer

The derivative of the function at \( x = 2 \) is \( 20 \).

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