please do the following problems and show the work

37. Sketch the graph of the function f(r) = 23 + 3x + 2. Sketch the tangent line to this graph at the point (1, 6). What is the slope of this tangent line? What is the equation of this tangent line? Notation 18 (Leibniz vs. Newton) The symbol _ means "take the derivative of the following function with respect to the domain variable r". This symbol is known as Leibniz notation and can be used interchangeably with the Newtonian notation introduced in Definition 16. In other words, If(x) = f(x). Note: A is called the derivative operator. The _ is applied to a function f and outputs another function f', which we call the derivative of f. Furthermore, ify = f(x) then y' = Ly= dy f ( x) = f(x). Definition 19 If the function f has a derivative at the domain value r, we say the function is differentiable at r. If a function is differentiable at every point in a particu- lar set, we say the function is differentiable on that set. If a function f is differentiable on its domain, then we simply say that f is differentiable. Theorem 20 (Linearity of the Derivative Operator) Taking the derivative is a linear operation. In other words, if f and g are differentiable at x and if A is any real number, then " (f(x) + g(x)) = Af' (x) + g'(x). 38. Prove Theorem 20 using the definition of the derivative and properties of limits. Theorem 21 If f is differentiable at r = a then f is continuous at r = a. 39. Prove Theorem 21. Give this theorem a name