Let f:R-R, where f(x)=3+6x-2x^3. a) determine the values of x for which the graph of f has positive gradient. b) find the values of x for which the graph of f has increasing gradient.

Question

Let f:R->R, where f(x)=3+6x-2x^3. a) determine the values of x for which the graph of f has positive gradient. b) find the values of x for which the graph of f has increasing gradient.

anonymous · Answer

in simpler language is this
a) find where the derivative is positive?

anonymous · Answer

yep i understood that, but i wasnt sure what to do next.

anonymous · Answer

$$f'(x)=6-6x^2=6(1-x^2)=6(1+x)(1-x)$$ a parabola that opens down. it will be positive between the zeros, namely on 
$$(-1,1)$$

anonymous · Answer

"increasing gradient" i take to mean the second derivative is positive.  so 
$$f''(x)=-12x$$ which is positive on 
$$(-\infty,0)$$ and negative on 
$$(0,\infty)$$

anonymous · Answer

thanks

anonymous · Answer

yw