Question

If f(x) = x^4 /2 + 3/2 x^3 +2x - 5
Then find f'(x) and f'(-2)​

Answer 1

Solution

Given:-

• f(x) = x⁴/2 + 3/2(x³) + 2x - 5

Find :-

• Value of f'(x) & f'(-2)

Explanation

We Have

$\dag\boxed{\underline{\tt{\red{\:\dfrac{dx^n}{dx}\:=\:nx^{n-1}}}}}$

Here ,

we can also denote of defferentation like that,

• d/dx f(x) = f'(x)

So, First differenciate f(x)

==> d f(x)/dx = d/dx [ x⁴/2 + 3/2x³ + 2x - 5]

==> f'(x) = 4/2 x³ + 9/2 x² + 2 - 0

Because ,

• d/dx (N) = 0 , [ N = Natural Number]

==> f'(x) = 2x³ + 9/2 x² + 2

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Now, Calculate f'(-2),

==> f'(-2) = 2×(-2)³ + 9/2 (-2)² + 2

==> f'(-2) = 2 × (-8) + 9/2 × 4 + 2

==> f'(-2) = -16 + 9×2 + 2

==> f'(-2) = -16 + 18 + 2

==> f'(-2) = 2 + 2

==> f'(-2) = 4

Hence

• Value of f'(-2) = 4

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