Chapter 1.1, Problem 26ES

Find the derivative of the function. 54 q(y)=4y² (2y²+1)

Find the derivative of the function. k(x) = − 6(5x +4) -

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Find all values of x for the given function where the tangent line is horizontal. 3 =√x³-12x² + 45x+5

Find the equation of the tangent line to the graph of the given function at the given value of x. 6 f(x) = x(x² - 4x+5)*; x=2

7. Suppose that X is a set, that I is a nonempty set, and that for each i Є I that Yi is a set. Suppose that I is a nonempty set. Prove the following:2 (a) If Y; CX for all i EI, then Uiel Yi C X. ¹See Table 4.8.1 in zyBooks. Recall: Nie X₁ = Vi Є I (x = X₁) and x = Uier X₁ = i Є I (x Є Xi). (b) If XCY; for all i Є I, then X Ciel Yi. (c) U(x)=xnUY. iЄI ΕΙ

Find the equation of the tangent line to the graph of the given function at the given value of x. f(x)=√√x+33; x=4

Find g[f(-7)]. f(x) = x² + 1; g(x)=-5x-1

Find the x-values where the following do not have derivatives.