So, week seven is complete. I'm finally getting the hang of stuff I had trouble with at the begining of the year. I'm ready to review and do allll those packets in class! haha
Derivatives are finally easy. So, I'm going to show a few examples of those:
1. f(x)=x^5tanx (this would be product rule)
x^5sec^2x+5x^4tanx
2. y=cos(2x^5+3) (this would NOT be product rule)
-sin(2x^5+3)*10x^4
-10x^4sin(2x^5+3)
Also, anything that says find the slope or derivative of the function, at a point or x-value is so easy too. Just take the derivative and then plug in the x-value. Now for an example:
1. Find the slope of the graph of the function f(x)=x(3x^4+2) at x=5.
x(3^4+2)
x(12x^3)+(3x^4+2)(1)
12x^4+3x^4+2
12(5)^4+3(5)^4+2= 9377
I'm still having trouble on optimization. I plan on getting someone to help/teach me with that. But my real question is I forgot how to find an equation of the tangent line. Can someone help me on that?
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the first step is take the derivative of the function that they give you. Then once you have done that, plug in the x value from the point they have given you. After you plug into the y-y1=(number you got when plugging in to derivative)(x-x1). Then you solve that function for y. Once you have done that, that equation that is solved for y is your answer. Hope this helps :)
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