In Problems 35-38, (a) find the slope of the tangent to the graph of f ( x ) at any point, (b) find the slope of the tangent at the given point, (c) write the equation of the line tangent to the graph of f ( x ) at the given point, and (d) graph both f ( x ) and its tangent line (use a graphing utility). f ( x ) = 5 x 3 + 2 ; ( − 1 , − 3 )
In Problems 35-38, (a) find the slope of the tangent to the graph of f ( x ) at any point, (b) find the slope of the tangent at the given point, (c) write the equation of the line tangent to the graph of f ( x ) at the given point, and (d) graph both f ( x ) and its tangent line (use a graphing utility). f ( x ) = 5 x 3 + 2 ; ( − 1 , − 3 )
Solution Summary: The author explains how the slope of the tangent can be evaluated by the derivative of f(x).
In Problems 35-38, (a) find the slope of the tangent to the graph of
f
(
x
)
at any point, (b) find the slope of the tangent at the given point, (c) write the equation of the line tangent to the graph of
f
(
x
)
at the given point, and (d) graph both
f
(
x
)
and its tangent line (use a graphing utility).
Which of the following is an equation of
the line tangent to the graph of
f (x) = -
= 3?
x³ + 4x2 at the point where
1. Given f(x) = –3x² – 5x + 1
(a) Evaluate f(1) and write as an ordered pair.
(b) What is the slope of the tangent line at the above point?
(c) Given Determine the equation of the line tangent to f(1).
If the point P=(9,−2) is on the graph of a function, and the slope of the graph at P is −8, then the slope-intercept form of the tangent line at P is y=
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