Find an equation of the tangent line to the graph of the function at the point that has x -coordinate . Hint : use point-slope formula to find the equation of the tangent line.

Question

Find an equation of the tangent line to the graph of the function  at the point that has x -coordinate  . Hint : use point-slope formula to find the equation of the tangent line.

Quizplus · Accepted Answer

First, we need to find the derivative of the function: 
f'(x) = 2x - 3

Then, we need to plug in the x-coordinate of the point of tangency (which is given as x = 4) into the derivative to find the slope of the tangent line at that point: 
f'(4) = 2(4) - 3 = 5

Now we have a point (4, 5) and a slope of 5, so we can use the point-slope formula to find the equation of the tangent line: 
y - 5 = 5(x - 4)

Simplifying, we get: 
y = 5x - 15

So the equation of the tangent line is: 
y = 5x - 15

Therefore, the answer is (C).

Find an Equation of the Tangent Line to the Graph