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Use the four step process to find the slope of the tangent line to the graph of the given function at any point.

F(x)= -10x^2+7x

Respuesta :

1) x=x+h→F(x+h)=-10(x+h)^2+7(x+h)
Using (a+b)^2=a^2+2ab+b^2, with a=x and b=h
F(x+h)=-10[(x)^2+2(x)(h)+(h)^2]+7x+7h
F(x+h)=-10(x^2+2xh+h^2)+7x+7h
F(x+h)=-10x^2-20xh-10h^2+7x+7h

2) F(x+h)-F(x)=(-10x^2-20xh-10h^2+7x+7h)-(-10x^2+7x)
F(x+h)-F(x)=-10x^2-20xh-10h^2+7x+7h+10x^2-7x
F(x+h)-F(x)=-20xh-10h^2+7h

3) [F(x+h)-F(x)]/h=(-20xh-10h^2+7h)/h
[F(x+h)-F(x)]/h=-20xh/h-10h^2/h+7h/h
[F(x+h)-F(x)]/h=-20x-10h+7

4) Lim h→0 [F(x+h)-F(x)]/h=Lim h→0 (-20x-10h+7)
Lim h→0 [F(x+h)-F(x)]/h=-20x-10(0)+7
Lim h→0 [F(x+h)-F(x)]/h=-20x-0+7
Lim h→0 [F(x+h)-F(x)]/h=-20x+7


Answer: The slope of the tangent line to the graph of the given funtion at any point is m=-20x+7

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