Q1.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)=
Answers
Step-by-step explanation:
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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