Question

If f(5) = 12, f ' is continuous, and 7 f '(x) dx 5 = 16, what is the value of f(7)? f(7) =

Answer 1

The value of function f(x) at x = 7 is f(7) = 28

For given question,

we have been given the value of function f(x) at x = 5.

f(5) = 12

We have been given that f'(x) is continuous on 5 and 7

Also, $\int\limits^7_5 {f(x)} \, dx =16$

We need to find the value of f(7)

Since ∀x, f'(x) = f'(x), f is a primitive function of f' .

And f ' is continuous

$\Rightarrow \int\limits^7_5 {f(x)} \, dx =16\\\\\Rightarrow [f(x)]_5^7=16$

⇒  [f(7) - f(5)] = 16

⇒ f(7) - 12 = 16

⇒ f(7) = 16 + 12

⇒ f(7) = 28

Therefore, the value of function f(x) at x = 7 is f(7) = 28

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