Question

if f(x)=4x^2 then value of c in (-1,3)for which f(3)-f(-1)/4 =f dash (c)​

Answer 1

Answer:

The value of c is 1.

Step-by-step explanation:

Step 1: If f(x) = 4x² , then the value of c in (-1, 3) for which

$\frac{f(3)-f(-1)}{4}=f^{\prime}(c)$

here, f(x) = 4x²

at x = -1,

f(-1) = 4 × (-1)² = 4 × 1 = 4 ...(1)

at x = 3,

f(3) = 4 × 3² = 4 × 9 = 36 ...(2)

Step 2 :Differentiating f(x) with respect to x, we get

f'(x) = 4 × 2 x²¯¹ = 8x

∴ f'(c) = 8c ...(3)

from equations (1) , (2) and (3)

$\begin{aligned}& \frac{f(3)-f(-1)}{4}=f^{\prime}(c) \\& \Longrightarrow \frac{36-4}{4}=8 c \\& \Longrightarrow c=1\end{aligned}$

Therefore the value of c is 1.

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