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Determine the slope of the tangent to the graph of y = 6x^4 +2x^3 +5 at the point (-1,-3)

Find the answer first using the deriavtive of the polynomial function.

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Adam S. | Professional and Proficient Math TutorProfessional and Proficient Math Tutor
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Q: Determine the slope of the tangent to the graph of y = 6x^4 +2x^3 +5 at the point (-1,-3)
 
The slope of the tangent line at that point will be the derivative equation of the graph evaluated at that point.
 
A) Differentiating with respect to x gives: dy/dx = 24x^3 + 6x^2. Evaluating this equation at (-1,3) gives a slope of -24 +6 = -18.
 
The equation of the tangent line will be of the form: y = dy/dx*x + yo.
 
The y - intercept can be found through the equation (y-yo)/(x-0)=slope.
 
yo=y-x*dy/dx -> yo= 3+1*-18=-15.
 
Therefore the tangent line equation at (-1,3) is y = -18x - 15. 
 
 
Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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y' = 24x^3 + 6x^2
 
y'(-1) = -24 + 6 = -18
 
Slope of tangent at (-1,-3) is -18.