Good evening,

can you please help me with those questions

1.

Find the values of constants a, b, and c so that the graph of y = ax + bx"+ cx has a local maximum at x = - 1, local minimum at x = - 3, and inflection point at ( - 2,2). . . . a = b =\\] C =] (Simplify your answers. Type integers or simplified fractions.)\fFind the average value of the function f(t) = (t - 8) on [0, 15]- . . . The average value of the function f(t) = (t - 8) on [0, 15] is (Simplify your answer.)Find the limit of the following. lim (14X2 + 3X - 14x2 - 2x) X - 00 lim (14X2 + 3x - 14x2 - 2x ) = (Simplify your answer.)The given figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is 2 units long. (a) Express the y-coordinate of P in terms of x. (Hint: Write an equation for the line AB.) (b) Express the area of the rectangle in terms of x. (c) What is the largest area the rectangle can have, and what are its dimensions? P(x, ?) A X X (a) The expression for the y-coordinate of P is (Type an expression using x as the variable.) (b) The expression for the area of the rectangle is (Type an expression using x as the variable.) (c) The large: area the rectangle can have is | square units. (Type an integer or a simplified fraction.) What are the dimensions of the rectangle having the largest area? O A. 7 X2 units O B. 1x - units O C. 1x2 unitsFind the total area of the shaded region. K The total area of the shaded region is (Simplify your answer.) . . . 20 16 y = 10 8 10 12 14 16 18 20