Question #dcf48

↳Redirected from "Suppose that I don't have a formula for #g(x)# but I know that #g(1) = 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Joshua Z.
Nov 20, 2017

True

Explanation:

A full cubic polynomial looks like this:
#f(x)=ax^3+bx^2+cx+d#

Let's write an equation that shows the roots of the function. Two of the roots are 0. Let's assume the third root is #b#.

#f(x)=x*x*(x-b)#

As you can see, two of the roots are equal to 0 and the other is equal to #b#.

Let's expand this equation:

#f(x)=x^2*(x-b)#

#f(x)=x^3-bx^2#

We can see that there are no linear (#cx#) or constant (#d#). Therefore, the statement is true. Hope this helps.

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