- #1

karush

Gold Member

MHB

- 3,269

- 5

If the derivative of a function f is given by

$$f'(x)=\frac{1}{5}(x^2-4)^5-x^2$$

how many points of inflection will the graph of the function have?solution find $f"(x)$

$$f''(x)=2x((x^2-4)^4-1)$$

at $f''(x)=0$ we have factored

$$2 x (x^2 - 5) (x^2 - 3) (x^4 - 8 x^2 + 17) = 0$$

then

$$x=0\quad x=\pm\sqrt{3}\quad \pm\sqrt{5}$$

so we have 5 points of inflectionok I was wondering if this could be solved strictly by observation

also I used the $W\vert A$ to get $ f"(x)$

the only thing I know about finding inflexions is they are zero points of the second direvative of a function

where concave <---> convex

$$f'(x)=\frac{1}{5}(x^2-4)^5-x^2$$

how many points of inflection will the graph of the function have?solution find $f"(x)$

$$f''(x)=2x((x^2-4)^4-1)$$

at $f''(x)=0$ we have factored

$$2 x (x^2 - 5) (x^2 - 3) (x^4 - 8 x^2 + 17) = 0$$

then

$$x=0\quad x=\pm\sqrt{3}\quad \pm\sqrt{5}$$

so we have 5 points of inflectionok I was wondering if this could be solved strictly by observation

also I used the $W\vert A$ to get $ f"(x)$

the only thing I know about finding inflexions is they are zero points of the second direvative of a function

where concave <---> convex

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