Question

EXAMPLE 6 Find an equation of the tangent line to the parabola y = x^2 - 6x + 8 at the point (1, 3). SOLUTION From the previous example, we know the derivative of f(x) = x^2 - 6x + 8 at the number a is f'(a) = 2a - 6. Therefore, the slope of the tangent line at (1, 3) is f'(1) = 2(1) - 6 = -4. Thus, an equation of the tangent line, shown in the figure, is y - 3 = -4(x - 1) or y = -4x + 7.

Name: example 6 find an equation of the tangent line to the parabola y x2 6x 8 at the point 1 3 solution from the previous example we know the derivative of fx x2 6x 8 at the number a is f a 2a 6 72973
Uploaded: 2022-02-18T13:31:55-08:00
Duration: 1 min 52 s
Channel: Harsha M
Description: example 6 find an equation of the tangent line to the parabola y x2 6x 8 at the point 1 3 solution from the previous example we know the derivative of fx x2 6x 8 at the number a is f a 2a 6 72973

          EXAMPLE 6
Find an equation of the tangent line to the parabola y = x^2 - 6x + 8 at the point (1, 3).

SOLUTION
From the previous example, we know the derivative of f(x) = x^2 - 6x + 8 at the number a is f'(a) = 2a - 6. Therefore, the slope of the tangent line at (1, 3) is f'(1) = 2(1) - 6 = -4.

Thus, an equation of the tangent line, shown in the figure, is y - 3 = -4(x - 1) or y = -4x + 7.

Added by Daisy M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Harsha M

02/18/2022

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Step 1: Find the derivative of the function \( y = x^2 - 6x + 8 \). Show more…

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EXAMPLE 6 Find an equation of the tangent line to the parabola y = x^2 - 6x + 8 at the point (1, 3). SOLUTION From the previous example, we know the derivative of f(x) = x^2 - 6x + 8 at the number a is f'(a) = 2a - 6. Therefore, the slope of the tangent line at (1, 3) is f'(1) = 2(1) - 6 = -4. Thus, an equation of the tangent line, shown in the figure, is y - 3 = -4(x - 1) or y = -4x + 7.