Explain why f(x)=4x^7+7x^3+9x-357 does not have a tangent line with a slope of 1.

Explain why f(x)=4x^7+7x^3+9x-357 does not have a tangent line with a slope of 1.

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we can take the derivative of it and try to make it equal 1

f(x)= 4x^7+7x^3+9x-357
f'(x)= 28x^6+21x^2+9 = 1
28x^6 +21x^2 +8 = 0 has the same effect

we can use synthetic division and trial and error to try to come to the roots...

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