Find the slope of the tangent of y= 3_at x=-2,3 and 5. 4x-1Find the derivative of each of the following. a) f(x) = 2 b) f(x) = TT3Determine the point(s) on the curve y = 3x - 5x where the slope of the tangent is 4.Find the second derivative of the following functions. a) f(x) = 2 + 3x2 -5xFind the second derivative of the following functions. 51 - b) 2c\fFind the intervals where the following function is increasing. f(x) =2 - 5x3 + 5x2Classify the intervals of concavity for the following function. 4x3 -5Find the intervals where the following function is concave up. f(x) =Eve+lSketch the function /(x)-x+5x'+8x-14.A cylindrical-shaped tomato can is to have a volume of 1500 ml. a) Determine the dimensions that will minimize the can's surface area. b) The manufacturing company has placed a restriction on the width of the can. If the diameter cannot exceed 12 om for packing purposes. does this alter the optimal dimensions of the can?A fast food restaurant chain wishes to market and produce an ice cream dessert for the launch of the next blockbuster movie release. The owner of the fast food chain hires a mathematician to produce the demand and cost functions for this ice cream dessert. Based on market trials and the projected monthly sales of x ice cream desserts, the demand function is found to be p(x)= 30000-x 15000 The total cost (in dollars) of producing x ice cream desserts is C(x)=3500+0.76x Remember, when you see the word marginal, we're being asked for the rate of change.a) Determine the marginal revenue for monthly sales of 5000 ice cream desserts.\fc) Determine the marginal profit for monthly sales of 5000 ice cream desserts