Find an equation of the tangent line to the curve at the point .

Question

Find an equation of the tangent line to the curve  at the point  .

Quizplus · Accepted Answer

To find the equation of the tangent line, we need to find the derivative of the function at the given point.

Taking the derivative of the function 11eaa3e5_5566_f33e_9f8f_5b141d6989d7_TB5971_11 with respect to x gives:

dy/dx = 3x^2 + 5x - 12

Evaluate this at the point x = 2:

dy/dx (at x=2) = 3(2)^2 + 5(2) - 12 = 10

This is the slope of the tangent line at the point (2,14).

Now we can use the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1,y1) is the point on the line.

Using the point (2,14) and the slope 10, we get:

y - 14 = 10(x - 2)

Simplifying this, we get:

y = 10x - 6

So the equation of the tangent line is 11eaa3e5_5567_4162_9f8f_e186008bc3e7_TB5971_11.

Find an Equation of the Tangent Line to the Curve