A calculator is allowed on this question. The functions f and g are differentiable functions of x. It is known that the derivative of f is given by f'(x) = x. ln x. It is also known that g(2) 3 and g' (2) 1. A curve in the xy-plane is defined as f(x) = (g(x))² = 4xy. Find the slope of this curve at the point (2, 3). Elimination Tool Select one answer A -1.077 B -0.577 C -0.538 D 0.923 =

If the second derivative of a function f is given byf" (x) = x (x - 1) (x + 2)“, then f has points of inflection when x =

The curve y = ax + bx +c passes through the point (1,8) and is tangent to the line y = 5x at the origin. Find a, b, and c. (Hint: You can find these numbers by doing a few things. You can plug (1,6) and the origin into y. You can find the derivative of y=f(x); what is the derivative of f(x) at the origin?

The derivative of function g(theta) is given by g'(theta)=5 cos(theta)-3 sin(theta) and satisfies g(0)=6. What is the value of g(pi).