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(solution) M157 HW 6 8E Day 1 Some Differentiation Rules #1 - recall that


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1. For some functions f and g, f'(2)=3 and g'(2)=5. Calculate h'(2) when

a. h(x) = g(x) - f(x)

b. h(x) = 2f(x) + g(x)

c. h(x) = 11g(x) + 1.76


2. Calculate the slope of the tangent line to the curve y=1/?x^2) at the point (1,1)

3. Calculate the derivative of f(x) = x^4 +2x^2 +5

5. For some functions f and g, f(2) = 1, g(2) = 7, f'(2) = 3, g'(2) = 5. Calculate h'(2) when

a. h(x) = g(x) * f(x)

b. h(x) = g(x) / f(x)

c. h(x) = 3g(x) + f(x)/2


6. Find the points in the x-y plane at which the tangent lines to the curve y=x^3 + 3x^2 are horizontal

10. Differentiate f(x) = ?x^3 - 6x +5)


M157 HW 6 8E Day 1 Some Differentiation Rules #1 - recall that first you must find the derivative function and then evaluate that function at the desired input

 

#2 ? to make this problem easier recall that ? 2 = || and since the problem focuses on (1,1) we can simplify this to

 

just . In addition, graph and the tangent line that you found the slope of in this problem

 

#3 ? by calculate the derivative recall that this means to find the derivative function ?()

 

#5 ? Just like for #1 we need to first find the derivative function and then evaluate that function at the desired point. In

 

this problem, notice that the product and quotient rules are recipes that use , ? , , ? in some mathematical

 

combination

 

#6 ? Recall that a horizontal line has a slope of 0

 

#11 ? use your calculator to sketch a graph of the given function near (1,2) and add in the tangent line to the graph.

 


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