Question

let f: R implies R be the continuous and differentiable function such f(x)=f(10-x) and slope of tangent at x=-5 is 2 then f'(5)+f'(15)=​

Answer 1

SOLUTION

GIVEN

Let f : R → R be the continuous and differentiable function such that f(x) = f(10 - x) and slope of tangent at x = - 5 is 2

TO DETERMINE

f'(5) + f'(15)

EVALUATION

Here it is given that f : R → R be the continuous and differentiable function such that f(x) = f(10 - x)

Now slope of tangent at x = - 5 is 2

∴ f'(-5) = 2 - - - - - - (1)

Again

f(x) = f(10 - x)

Differentiating both sides with respect to x we get

f'(x) = - f'( 10 - x) - - - - - (2)

Putting x = 5 we get

f'(5) = - f'( 10 - 5)

⇒ f'(5) = - f'( 5)

⇒ 2f'(5) = 0

⇒ f'(5) = 0

Again Putting x = - 5 in Equation 2 we get

f'( - 5) = - f'( 10 + 5)

⇒ f'( - 5) = - f'( 15)

⇒ 2 = - f'( 15)

⇒ f'( 15) = - 2

Thus we get

f'(5) + f'(15)

= 0 - 2

= - 2

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