The area of a triangle with sides of length a, b, and c is given by a formula from antiquity called Heron's formula, shown below, where s = (a + b +c)/2 is the semiperimeter of the triangle. A = s(s- a)(s-b)(s-c) Complete parts (a) through (c) below. a. Find the partial derivatives A, Ap, and Ae: - a + ab? + ac A, = 8/s(s - a)(s - b)(s - c) (Type an expression using s, a, b, and c as the variables.) -b +a'b+ bc? A, = 8 s(s - a)(s - b)(s - c) (Type an expression using s, a, b, and c as the variables.) -c +a?c+b?c A. = 8 s(s - a)(s - b)(s - c) (Type an expression using s, a, b, and c as the variables.) b. A triangle has sides of length a = 3, b = 5, c = 7. Using the partial derivatives found in part (a), estimate the change in the area when a increases by 0.03, b decreases by 0.08, and c increases by 0.6. The change in area is approximately -0.06. (Round to three decimal places as needed.)