Question

Write an equation of the tangent line to the graph of y=f(x) at the point on the graph where x has the indicated value. f(x)=−7x²+9​/2x−3,x=0

Answer 1

The equation of the tangent line at the point is y = 9/2x - 3

How to determine the equation of the tangent line

From the question, we have the following parameters that can be used in our computation:

f(x) = −7x² + 9​/2x − 3

Also, we have

x = 0

Calculate f(0)

f(0) = −7(0)² + 9​/2(0) − 3

f(0) = -3

Differentiate the function to calculate the slope m

So, we have

m = -14x + 9​/2

Set x = 0

m = -14(0) + 9​/2

m = 9​/2

The equation of the tangent line is then calculated as

y = m(x - X) + f(X)

So, we have

y = m(x - 0) + f(0)

This gives

y = 9/2(x - 0) - 3

Expand

y = 9/2x - 3

Hence, the equation is y = 9/2x - 3