Chapter 2: Q. 95 (page 186)

Use the mathematical definition of a tangent line and the point-slope form of a line to show that if f is differentiable at $x = c$ , then the tangent line to f at $x = c$ is given by the equation $y = f' (c) (x - c) + f (c) .$

Short Answer

Expert verified

Ans:

$y - f (c) = f' (c) [x - c] y = f' (c) [x - c] + f (c)$

Step by step solution

Step 1. Given information:

Consider a function: $f (x)$

Here the objective is to show that the equation of the tangent line at any point $x = c$ is

$y = f (c) [x - c] + f (c)$

Step 2. Showing that if f is differentiable at x=c:

Let the derivative of the function is $f' (x)$ .

At point $x = c$ the slope of the tangent line is: $f' (x)$ and the value of the function is: f(c) Therefore equation of the tangent line at $(c, f (c))$ with slope $f' (x)$ is:

$y - f (c) = f' (c) [x - c] y = f' (c) [x - c] + f (c)$

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Use the mathematical definition of a tangent line and the point-slope form of a line to show that if f is differentiable at $x = c$ , then the tangent line to f at $x = c$ is given by the equation $y = f' (c) (x - c) + f (c) .$

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Showing that if f is differentiable at x=c:

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Use the mathematical definition of a tangent line and the point-slope form of a line to show that if f is differentiable at x=c, then the tangent line to f at x=cis given by the equation y=f'(c)(x−c)+f(c).

Short Answer

Step by step solution

Step 1. Given information:

Step 2. Showing that if f is differentiable at x=c:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

Use the mathematical definition of a tangent line and the point-slope form of a line to show that if f is differentiable at $x = c$ , then the tangent line to f at $x = c$ is given by the equation $y = f' (c) (x - c) + f (c) .$