Given that the graph of f(x) passes through the point (3, 7) and that the slope of its tangent...

Question:

Given that the graph of {eq}f(x) {/eq} passes through the point {eq}(3, 7) {/eq} and that the slope of its tangent line at {eq}(x, f(x)) {/eq} is {eq}2x + 5 {/eq}, find {eq}f(2) {/eq}.

Tangent Line:

The equation of the tangent line to a function f(x) at a point (x0,y0) is found linearizing the function at that point, i.e

{eq}y(x) = f(x_0) + f'(x_0)(x-x_0) {/eq}

where the ' symbol denotes the first derivative operation.

Answer and Explanation:

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We know that the slope of the tangent line to the function f(x) at point {eq}(x, f(x)) {/eq} is equal to the first derivative of the function

{eq}...

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Linearization of Functions

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Chapter 10 / Lesson 1
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Over the river and through the woods to Grandmother's house we go ... Are we there yet? In this lesson, apply linearization to estimate when we will finally get to Grandma's house!


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