216k views
0 votes
What is the answer and steps needed to solve part B? “Write an equation for the tangent line to the graph of f at x=7”

What is the answer and steps needed to solve part B? “Write an equation for the tangent-example-1

1 Answer

5 votes

The equation for the tangent line to the graph of f at x=7” is y - 0.5 = -0.5(x - 7).

Steps to solve:

Find the slope of the tangent line: The slope of the tangent line at a point is equal to the derivative of the function at that point. Since we are given that x = 7, we need to find f'(7).

Unfortunately, the graph of f is not given in the image, so we cannot directly calculate the derivative.

Use the table of values: However, the table of values provides some information about the derivative of f.

We can see that f'(5) = -2.455. We know that the graph of f has a horizontal tangent line at x = 4, which means that f'(4) = 0.

Estimate the slope: Since the graph is concave down for 0 < x < 6, we know that the derivative f'(x) is decreasing in this interval.

Therefore, we can estimate that f'(7) is somewhere between f'(5) = -2.455 and f'(4) = 0.

A reasonable estimate for the slope of the tangent line at x = 7 would be -0.5.

Find the y-intercept: The tangent line passes through the point (7, 0.5).

We can use the point-slope form of linear equations to find the equation of the tangent line:

y - y1 = m(x - x1)

where:

m is the slope of the tangent line (we estimated m to be -0.5)

(x1, y1) is the point on the tangent line (we know (x1, y1) = (7, 0.5))

Plugging these values into the equation, we get:

y - 0.5 = -0.5(x - 7)

Therefore, the equation of the tangent line to the graph of f at x = 7 is y - 0.5 = -0.5(x - 7).

User Alessandro Carughi
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories