Sample bartleby Q&A Solution
You ask questions, our tutors answer
Browse
Question

Need answer to the following question.

Find the equation of a tangent line to a curve given by
f(x) = 3x3 + 2x2 +x+1at x =1.
Transcribed Image Text

Find the equation of a tangent line to a curve given by f(x) = 3x3 + 2x2 +x+1at x =1.

Expert Answer

We first find the slope of the tangent for which we need derivative of f(x).  Differentiating f(x) w.r.t. x we get:

Now, slope is the value of f’(x) at the given point x = 1.

Now, to find any one point on the tangent line, we consider the fact that tangent line is drawn at x=1. This point also lies on the curve and hence its y-coordinate is the value of f(x) at x=1. We get:

Equation of a line in slope-point form is given as, (y y1) = slope * (x x1). Substituting the values of slope, x1 and y1, we get:

Answer: The equation of tangent line to the given curve at x = 1 is: