Question

Let f(x)=x^2-2x+1
a.Find the derivative f of f
b.find the point on the graph of f where the tangent line to the curve is horizontal.
c.Sketch the graph of f and the tangent line to the curve at the point found in part (b).
d. Sketch the graph of f and the tangent line to the curve at (-1,-1/2).
"Please show steps"

Answer 1

Answer:

a.) f'(x) = 2x - 2

b.) horizontal tangent line at (1, 0)

c.) view image

d.) the point given, (-1, -1/2), isn't even located on the graph of f(x). Either there is a typo or the question is poorly stated.

Step-by-step explanation:

a.) You should know how to do derivative already

b.) Horizontal tangent line just mean that the slope is zero. Since a derivative is a slope, just find when the derivative is equal to 0.

c.) The function f(x) looks like a U. The only spot that has a zero slope is at the bottom of the U when the slope changes from negative to positive. Since my horizontal tangent line(where the slope is 0) is located at point (1,0), that must be where the bottom of the graph is,

d.) Poorly stated question. The point given isn't even located on the graph.