SOLUTION: Find the slope and the equation of the tangent line to the graph of the function at the given value of x. f(x)=x^4-17x^2+16; x=1 PLEASE SOLVE A & B from the question above.

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Question 1191024: Find the slope and the equation of the tangent line to the graph of the function at the given value of x.
f(x)=x^4-17x^2+16; x=1
PLEASE SOLVE A & B from the question above.
A) The slope of the tangent line is
B) The equation of the tangent line is y=

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20849) (Show Source):
You can put this solution on YOUR website!
;
Find the first derivative and evaluate at to find a slope of the tangent line.
.
'

'

Now that we have a slope for the tangent line, we need to identify a point on the line.
We know the tangent line touches the function at the point , so let's find the value of at this point:

So we know the tangent line goes through the point(,)

Finally, we can use the point-slope formula for a line to find the equation of the tangent line.

To find the value of , substitute the values we have calculated for the point and slope of the tangent line:

the equation of the tangent line is:

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

At x=1, we have f(1)=1-17+16=0, so the point of tangency is (1,0)

To find the slope at (1,0), evaluate the derivative of the function at x=1.

f'(x)=4x^3-34x
f'(1)=4-34=-30

The slope at x=1 is -30.

Plug (x,y)=(1,0) and slope m=-30 into either the point-slope or slope-intercept form of the equation of a line to find the equation of the tangent is y=-30x+30.

A graph with x on (-2,2) and y on (-20,20):