Question

How do you find the tangent line for this equation and then find its slope given `y=-2x^5 - 7x^3 + 8x^2` at x=1?

Answer 1

Slope of tangent is `-31` and equation of tangent is `31x+y=30`

Explanation:

As `y=-2x^5-7x^3+8x^2`,

at `x=1`, we have `y=-2-7+8=-1`

Hence, we are seeking tangent at point `(1,-1)` on the curve.

We do not first find the equation of the tangent and then its slope. In fact, we find its slope first and then using point slope form of equation, we find the equation of tangent.

Nowslope of tangent is given by the value of its first derivative at that point.

As first derivative of `y=-2x^5-7x^3+8x^2` is `-10x^4-21x^2`,

the slope of tangent is `-10*1^4-21*1^2=-10-21=-31`

and equation of tangent is `(y-(-1))=-31(x-1)`

or `y+1=-31x+31` i.e. `31x+y=30`