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Sketch a graph of function $f$ that satisfy all the following conditions

$f'(x)>0 \,\text{if} -3<x<3 \,\text{or}\, x>6 ;\\ f'(x)=e^{(2x+7)} \,\text{if} \,x<-3 ;\\ f'(x)=-3 \,\text{if}\, 3<x<6 ;\\ f''(x)>0 \,\text{if} \,0<x<3 ;\\ f''(x)<0 \,\text{if} -3<x<0\, \text{or} \,x>6 ;\\ \displaystyle\lim_{x\to -\infty} f(x)=-15 ;\\ \displaystyle\lim_{x\to\infty} f(x)=12 ;\\ f \,\text{is continuous on} (-\infty, \infty) ;\\ f \,\text{is not differentiable at}\, x=3 \,\text{and}\, x=6 ;\\ f(0)=f(6)=0$

SarGe
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Anonymous
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    Hello Amanda, welcome to Math.SE. Please format your questions with MathJax, as this will attract more positive attention toward your question and make it more readable. Anyway, what have you tried? Where are you stuck? – morrowmh Jun 20 '20 at 07:59
  • Hello Michael, I am stuck at sketching the graph and I can't seem to plot the graph with all the information given. I have identify the increasing where f'(x)>0 , concave upward and concave downward. – Anonymous Jun 20 '20 at 13:20

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