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How do you find the slope of the secant lines of #f(x)=x^3-12x+1# through the points: -3 and 3?

Answer 1

Emily Ammerman

slope #=-3#

Given : #f(x)=x^3-12x+1#

when #x=-3# find #f(-3)#

#f(-3)=(-3)^3-12*(-3)+1=-27+36+1=10#

We have a point #(-3, 10)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ when #x=3# find #f(3)#

#f(3)=(3)^3-12*(3)+1=27-36+1=-8#

We have a point #(3, -8)# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Solve the slope Slope#=(y_2-y_1)/(x_2-x_1)=(10--8)/(-3-3)=18/-6=-3#

God bless....I hope the explanation is useful.

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Answer 2

Ezekiel Alexander

To find the slope of the secant line between two points on the graph of a function ( f(x) ), you use the formula:

[ \text{Slope} = \frac{f(x_2) - f(x_1)}{x_2 - x_1} ]

Given ( f(x) = x^3 - 12x + 1 ) and the points ( x_1 = -3 ) and ( x_2 = 3 ):

[ \text{Slope} = \frac{f(3) - f(-3)}{3 - (-3)} ]

[ \text{Slope} = \frac{(3)^3 - 12(3) + 1 - ((-3)^3 - 12(-3) + 1)}{3 - (-3)} ]

[ \text{Slope} = \frac{27 - 36 + 1 - (-27 + 36 + 1)}{6} ]

[ \text{Slope} = \frac{27 - 36 + 1 + 27 - 36 - 1}{6} ]

[ \text{Slope} = \frac{2(27) - 2(36)}{6} ]

[ \text{Slope} = \frac{54 - 72}{6} ]

[ \text{Slope} = \frac{-18}{6} ]

[ \text{Slope} = -3 ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.