Please indicate if each statement is true or false and if false please explain why

If the graph of a function has three x intercepts, then it must have at least two points at which its tangent line is horizontal.

If f'(x) = 0 for all of x in the domain of f, then f is a constant function.

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If the graph of a function has three x intercepts, then it must have at least two points at which its tangent line is horizontal.

Response: If you draw a simple "curved" function that intercepts the x-axis three times, you will find that it has two "humps." One hump looks like an upside down "U" ...

Solution Summary

This is a proof regarding the intercepts and horizontal tangent lines of a function.

... The question didn't ask you to prove the binomial theorem, but you can prove it using induction on n. The proof is below (I got it from Wikipedia), and ...

Please see attachment All the questions. ... in a proof, deriving a formula for the nth derivative of the ...Question #1 ∞ n +1 ∑ 3n i. The series diverges 2 + 5n ...

... in a proof, deriving a formula for the nth derivative of the product of two functions, and a set of three proofs regarding concavity. Question #1 ∞ n +1 ...

... The proof of the result used is by mathematical induction on 'n'. ... That is ﬁnd a formula for f (n) (x). Question Find a formula for the n-th derivative of f ...

... Here are the answers to your questions. ...Question b In the steady state, the growth of output should ... I will use the following notation: the derivative of a ...

... Specifically, there are three questions: 1. Production theory 2. Game ... Now the remaining question is MRTS ... I use the following two rules of differentiation: 1. if ...

Elementary Calculus: Integers, Derivatives, 14 Questions. ... x) = x 2 − 4 is a continuous function Proof. ... of the following functions using differentiation rules. ...

... but is reversible I have a question about relations ...Proof So you need a mathematical proof that the ... The remaining partial derivative can be expressed in more ...

... Finally, we can infer that: ( 18) (The complete proof by induction is similar to the previous one). ...Question 8. Write f (n) (x) for the nth derivative of f ...

... of theta subscript x - f''''' is the fifth derivative. Please answer question fully and clearly explaining every ... Please see the attachment for detailed proof. ...