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.

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.

Solution

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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