Find an equation of the tangent line to the curve at the point (-1,1) if y=4x^cubed +5x

Question

anonymous · Answer

tan = y/x
tan = -1/1

anonymous · Answer

$$y=4x^3+5x$$
$$y'=12x^2+5$$ you want the slope at x = -1, get 
$$12(-1)^2+5=12+5=17$$ so slope is 17, point is (-1,1) use point slope formula

anonymous · Answer

$$y-1=17(x+1)$$

anonymous · Answer

how did you get from y=4x^3 +5x to y=12x^2+5?

jim_thompson5910 · Answer

he took the derivative of y = 4x^3+5x to get y' = 12x^2+5

anonymous · Answer

what about synthetic division?

jim_thompson5910 · Answer

no you cannot use synthetic division to get the derivative

anonymous · Answer

I already told you the answer is 3.141592654

jim_thompson5910 · Answer

they want an equation, not just the slope

jim_thompson5910 · Answer

besides, the answer isn't pi

anonymous · Answer

?

anonymous · Answer

you have to use the derivative to find the slope.  there is no other way to find the slope of a tangent line that i know of.  it doesn't have a definition with out the derivative

anonymous · Answer

I figured it wasn't pie. im using the Slope = the limit of x of approaches a to use the formula f(x) -f(a)/ x-a..... the answer is y=7x+8

jim_thompson5910 · Answer

answer should be $$\large y=17x+18$$