a) b) 54-1+1 Use logarithmic differentiation to find the first derivative of y= (3x² +2) 13 Evaluate the integration I, where I = dt 5t2 3 If f'(x) == Vx+ and the curve f(x) passes through the point (0,2) 2 2 i) Find f(x) 11) Find the local extreme (if any) of f(x) using second derivative test. d) Evaluate using integration by parts: 5 (0)do, where f(O)=(0+1) sin 30 Page 4 of 5
a) Verify the Rolle's theorem for the function f(x) = -1 x +x-6 over the interval (-3, 2] 3-X b) Find the absolute maximum and minimum values of function f(x)= (1+x?)Ě over the interval [-1,1] c) Find the following for the function f(x) = 2x – 3x – 12x +8 i) Intervals where f(x) is increasing and decreasing. ii) Local minimum and local maximum of f(x) iii) Intervals where f(x) is concave up and concave down. iv) Inflection point(s). v)...
D1.1. Evaluate f'(a) by using the definition of derivative of a function f(x) = 4x2 + 3x – 5 at a = -2. [4 Marks] D1.2. (a) Find the derivative of y = 4 sin( V1 + Vx). (b) If y = sin(cos(tan(x2 + 3x – 2))), then find the first derivative. [3 Marks] D1.3. Using logarithmic differentiation, find the derivative of y = (sec x)+”.
Use logarithmic differentiation to find the derivative of the function. y = (tan(x))2/ 4 cos ec(2x) y' = 2 ln(tan(x)) 2 Need Help? Read It Watch It Talk to a Tutor Submit Answer 13. [1/1 Pointsi TOT
Use logarithmic differentiation to evaluate f'(x). f(x) = (x + 3)10 / (4x - 4)12 f'(x) = _______
Calculus 1 MAT 201 Final Exam, Spring 1 2019, LAGCC Evaluate the following limits, you may use L'Hospital's rule, if it applies. -V31+4 lim 4-1 -4 a. b. Evaluate the following limit. lim xIn x x-0 2. Evaluate and explain your answer -xsin(x)+cos (x) x+1 130 dx (a.) 130 Differentiate each of the following below using the fundamental theorem of calc part 1 X cos? (1- 51) dt ) g (x) = S_ e (2c) g(t)= J x2t+1 3 Use...
10. f(x) = logs (sec(4x' - 2x + 5)) Chapter 4 - Applications of the Derivative 11. Given the function f(x) = 2x - 3x2 - 12x + 5 Find critical points (including relative minimums/maximums, if applicable), where the function is rising and falling, where it is concave up and down, any points of inflection. Summarize below. a. f(x) = b. f'(x) = c. Inflection points (give as points) d. Local MAXs (give as points): e. Local MINs (give as...
Problem 1. (a) The radius of a sphere is increasing at a rate of 4 mm/s. How fast is the volume increasing when the diameter is 80 mm? dy dx (b) If x+y+z-9, dt 5, and -4, find dt dz dt when (x, y, z)-(2,2,1). Problem 2. (a) Find the derivative of the function yr e-****** (b) Find the derivative of the function y - In(x* +100). cos. Problem 3. Use logarithmic differentiation to find the derivative of the function...
7. Use the Logarithmic laws to simplify y first and then find the derivative y'. 5 x +3 (a) y = log1 (3+5)4 (b) y = log (1+) 8. Use logarithmic differentiation to find y' if y = 3+ (x - 2) x41x + 5 (b) y = a. 12.0 (C) y = (1+ (Use the result of Q7(b))
6. o 1 points Use logarithmic differentiation or an alternative method to find the derivative of the function y=x8 cos x Submit Answer Save Progress 6. o 1 points Use logarithmic differentiation or an alternative method to find the derivative of the function y=x8 cos x Submit Answer Save Progress