Answered

Find the best solutions to your problems with the help of IDNLearn.com's experts. Join our interactive Q&A community and access a wealth of reliable answers to your most pressing questions.

Find the slope and equation of the tangent line to the graph of the function at the given value of x.

f(x)=x^4-20x^2+64;x=-1

Sagot :

Olemakpaduidn
The slope is the differential of the function.

Recall, if y = x^n,  (dy/dx) =  nx^(n-1).

y=x^4-20x^2+64;  x = -1.  To differentiate this, we do it for each term.

(dy/dx) = (4)(x^(4 -1))  - (2)(20x^(2-1) + 0*64x^(0-1)        (Note 64 = 64x^0, x^0 =1)
           =  (4)x^(3) - 40x^(1)  + 0
            =    4x^3  -  40x^1. 

(dy/dx)  =    4x^3  -  40x.   Note at x = -1.


(dy/dx), x = -1,   =     4(-1)^3  -  40(-1)                         
                         =    -4 +  40  = 40 - 4 = 36.

Slope at x = -1 is 36.
Cheers.

We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. IDNLearn.com provides the best answers to your questions. Thank you for visiting, and come back soon for more helpful information.