Two spherical pieces of cookie dough have radii of 3cm & 5cm. The pieces are combined to form one large spherical piece of d
1 answer:
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Given
To find the derivative of the give function,we apply below exponent rule first:
So,
Next, we apply the chain rule:
So,
We substitute back u=(5x-6):
Simplify:
Therefore, the answer is:
Answer:
The fifth degree Taylor polynomial of g(x) is increasing around x=-1
Step-by-step explanation:
Yes, you can do the derivative of the fifth degree Taylor polynomial, but notice that its derivative evaluated at x =-1 will give zero for all its terms except for the one of first order, so the calculation becomes simple:
and when you do its derivative:
1) the constant term renders zero,
2) the following term (term of order 1, the linear term) renders: since the derivative of (x+1) is one,
3) all other terms will keep at least one factor (x+1) in their derivative, and this evaluated at x = -1 will render zero
Therefore, the only term that would give you something different from zero once evaluated at x = -1 is the derivative of that linear term. and that only non-zero term is: as per the information given. Therefore, the function has derivative larger than zero, then it is increasing in the vicinity of x = -1