Question

The slope of the tangent line to the curve y=f(x) at the point (c, f(c)) is

Answer 1

Answer:

ANSWER

f

′

(x)=2x+1

∫f

′

(x)dx=∫(2x+1)dx

f(x)=x

2

+x+c passes through (1,2)

2=2+c→c=0

So, f(x)=x

2

+x

0

∫

1

(x

2

+x)dx

1/3+1/2=5/6squnits.

Answer 2

Concept:

The tangent line (or simply tangent) to a plane curve at a particular location is a straight line that "just touches" the curve at that point, according to geometry. At a particular location, the tangent reflects the instantaneous rate of change of the given function. As a result, the slope of the tangent at a given position is equal to the function's derivative at that same location.

Given:

The curve y = f(x).

Point (c, f(c)).

Find:

The tangent slope at point (c, f(c)).

Solution:

The slope of the tangent is the differentiation of the curve.

y' = f'(x).

The slope of the tangent at the point (c,  f(c)) is,

Substitute value c in x.

y' = f'(c).

Hence, f'(c) gives the slope of the tangent at the point (c, f(c)).