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Suppose that the second derivative of a function  f  is given by

f''(x)=x^(7)(x-2)^(2)(x-3)^(9)

Find the x-coordinates of the inflection points of  f  (if any).

(A) 0 and 3 only (B) none (C) 0 and 2 only (D) 3 only (E) 2 only (F) 0,2, and 3 (G) 0 only (H) 2 and 3 only

User Robson
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1 Answer

2 votes

Answer:

Hello,

Explanation:


f''(x)=x^7*(x-2)^2*(x-3)^9\\\\\begin{array}---&-&-&-&-&-&-&-\\x&&0&&2&&3&\\x^7&-&0&+&+&+&+&+\\(x-2)^2&+&0&+&+&+&+&+\\(x-3)^9&-&-&-&-&-&0&-\\---&-&-&-&-&-&-&-\\f''(x)&+&0&-&0&-&0&+\\&&Inf&&Max&&Inf&\\---&-&-&-&-&-&-&-\\\end{array}

Answer A: 0 and 3

2 is a maximum.

Suppose that the second derivative of a function  f  is given by f''(x)=x^(7)(x-2)^(2)(x-example-1
Suppose that the second derivative of a function  f  is given by f''(x)=x^(7)(x-2)^(2)(x-example-2
User Kayteen
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