- 6x + 2 on the domain [-7,2]. Find the absolute extrema if they exist, as well as all values of x where they occur, for the function f(x)= x³ + x²- 2 Find the derivative of f(x) = - 6x + 2. f'(x) =
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- using the definition of derivative to find f'(x) for the function:f(x)=4/x. How do I solve this?Equation of the line tangent to the graph of f(x)=(x)(1-2x)^3 at (-1,1).A derivative formulaa. Use the definition of the derivative to determined/dx(ax2 + bx + c), where a, b, and c are constants.b. Let ƒ(x) = 4x2 - 3x + 10 and use part (a) to find ƒ′(x).c. Use part (b) to find ƒ′(1).
- f and g are differentiable functions that sum is a constant ( f (x) + g(x) = k for all x) what can be concluded about their graph and or derivatives?find the general solution of the equation Indicate the open version of the derivative operators step by step//show the step by step a).Find x value where the graph has a horizontal tangent line. f(x) = x^3 + x Using the fact that derivative is the slope of the tangent line, and the horizontal line has slope 0, solve the equation f ′ = 0 to determine if the tangent line is horizontal for any x-value.
- On [-8,0] the value of the first derivative of f(x)= x^2 is positive. True or False?Given the function f(x) = 3cos(x/2), find the relative extrema on the interval (pi, 7pi) using the First Derivative Test and the Second Derivative Test. Compare the results. Graph the function with the relative extrema.Find an equation of the tangent line to the graph of the function f through the point (x0, y0) not on the graph. To find the point of tangency (x, y) on the graph of f, solve the equation f′(x) = (y0 − y)/(x0 − x) f(x) = 2/x (x0, y0) = (5, 0)
- Find the first and second derivative of (x^3-3x^2+5)/(x^3+1). I found the first derivative, I believe it is correct. I got: (3x(x^3-4x-2))/(x^3+1)^2 I'm just having a harder time with the second derivative. For that I got (3(3x^8-10x^6+24x^4+12x^3+3x^2-4))/((x^3+1)^2)^2An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corners and bending up the sides. Find the dimensions of the resulting box that has the largest volume. Find the volume of the open box as a function of x where x represents the height of the box Find the first derivative of the open box, with respect to x Find the dimensions of the resulting box that has the largest volume