The attachment is hints and directions from the professor. Thank you!
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
#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.
This question was answered on: Jan 30, 2021
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