Question #7ae0c

1 Answer
Jan 31, 2018

See below.

Explanation:

#f(x)=x^4#

Since we have the instantaneous rate of change at #x=-1# namely #-4#. This is also the gradient of the tangent line at #x=-1#

We need the corresponding value of #y# at #x=-1#. So using:

#f(x)=x^4#

#y=(-1)^4=1#

So we have the coordinates of a point on the line:

#(-1,1)#

Using point slope of a line:

#(y_2-y_1)=m(x_2-x_1)#

Where #m# is the gradient:

#y-1=-4(x-(-1))#

#color(blue)(y=-4x-3)#

GRAPH:

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