SOLUTION: Consider the function f(x) = -x2 + 27x − 9. The slope of the tangent line to f(x) at x = -9 is ? The value of f(x) at x = -9 is ? The y-intercept of the tangent line at

Algebra ->  Finance -> SOLUTION: Consider the function f(x) = -x2 + 27x − 9. The slope of the tangent line to f(x) at x = -9 is ? The value of f(x) at x = -9 is ? The y-intercept of the tangent line at       Log On


   

Question 1179793: Consider the function f(x) = -x2 + 27x − 9.
The slope of the tangent line to f(x) at x = -9 is ?
The value of f(x) at x = -9 is ?
The y-intercept of the tangent line at x = -9 is ?

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Consider the function
f%28x%29+=+-x%5E2+%2B+27x+-+9+
The slope of the tangent line to f%28x%29 at x+=+-9 is ?
find derivate
f'%28x%29+=+-2x+%2B+27........plug in x+=+-9
f'%28-9%29+=+-2%28-9%29+%2B+27
f'%28-9%29+=45
=> slope is 45
The value of f%28x%29+ at x+=+-9 is ?



f%28-9%29+=+-%28-9%29%5E2+%2B+27%28-9%29+-+9+
f%28-9%29+=-333
=> tangent point: (-9,-333)=(x%5B1%5D,y%5B1%5D)
The y-intercept of the tangent line at x+=+-9 is -333
tangent line will be:
y-y%5B1%5D=m%28x-x%5B1%5D%29
y-%28-333%29=45%28x-%28-9%29%29
y%2B333=45%28x%2B9%29
y%2B333=45x%2B405
y=45x%2B405-333
y+=+45+x+%2B+72

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