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- Use the graph to estimate the slope of the tangent line to y = x" at the given point. Verify your answer analytically. (a) y = x1/2, (9, 3) 10 8 y 4- (9, 3) 2- 4 6 8 10 y' = 3Ex. 4) For F and G functions and given that: F(5)=-1,F"(5)=-3 G(5) = 4 G'(5) = 2 a) If P(x) = F(x)· G(x), then evaluate P'(5). P'(5) = F(x) b) If Q(x) = G(x) then evaluate Q'(5). Q'(5)=_If P(A or B) = 0.801, P(B') = 0.33 and P(A and B) = 0.20. Find i) P(B) ii) P(A)
- The tangent line to y=f(x)y=f(x) at (−3,−2)(−3,−2) passes through the point (−4,−3)(−4,−3). Compute the following. f(-3)= f'(-3)=Ex. 5) For R and Q functions and given that: Q(-1) = 5, R(-1) = -4, R(5) = 7; || Q'(-1) =-3, R'(-1) =2, R'(5) =-1 If f(x) = R(Q(x)), then evaluate f"(-1). f"(-1)=Find G′(w) if G(w)=5/ 9w^5 +7 sqaure root w. G'(w)
- Find f' (x) and simplify. f(x) = 4x° In x Which of the following shows the correct application of the product rule? O A. (4x) +(In x) (12x?) B. (4x°) (12x) +(In x) OC. G(12*) OD. (4x°)-(Inx)(12x²)For the function f(x) = 7x° – 5x + 2x + 7, find f''(x). Then find f''(0) and f"(5). f'"(x) = Select the correct choice below and fill in any answer boxes in your choice. A. f'(0) = (Simplify your answer.) O B. f'(0) is undefined. Select the correct choice below and fill in any answer boxes in your choice. A. f''(5) = (Simplify your answer.) B. f''(5) is undefined.Find the value of dy/dx at the point (-2, 1) for the function which is defined implicitly by x²y у -= 6 а. -2.5 b. 0.4 c. 6 d. 2.5 е. -0.4