2. (2 points) use the figure to find the values of a, b, c, and d about f at p, where f(a)=b and f(c)=d\na =…

2. (2 points) use the figure to find the values of a, b, c, and d about f at p, where f(a)=b and f(c)=d\na = \n\nb = \n\nc = \n\nd = \n\n3. (5 points) let f(x)=2x^{2}-4x + 6. find the derivative f(x) by using the definition of the derivative of f as a limit of a difference quotient, and use algebraic calculations to compute the limit.

2. (2 points) use the figure to find the values of a, b, c, and d about f at p, where f(a)=b and f(c)=d\na = \n\nb = \n\nc = \n\nd = \n\n3. (5 points) let f(x)=2x^{2}-4x + 6. find the derivative f(x) by using the definition of the derivative of f as a limit of a difference quotient, and use algebraic calculations to compute the limit.

Answer

Explanation:

Step1: Identify the value of (a)

(a) is the (x) - coordinate of the point (P). From the figure, the point (P) has coordinates ((4,1)), so (a = 4).

Step2: Identify the value of (b)

Since (f(a)=b) and (a = 4), (b) is the (y) - coordinate of the point on the function (y = f(x)) at (x=a). For (x = 4), from the point (P(4,1)) on (y = f(x)), (b = 1).

Step3: Identify the value of (c)

(c) is the (x) - coordinate at which we are finding the derivative. The derivative (f^{\prime}(c)) is evaluated at the (x) - coordinate of the point of tangency. The point of tangency is (P) with (x) - coordinate (4), so (c = 4).

Step4: Find the value of (d)

(d=f^{\prime}(c)) and (c = 4). The slope of the tangent line at the point ((x_1,y_1)=(4,1)) and another point ((x_2,y_2)=(2,5)) on the tangent - line can be found using the slope formula (m=\frac{y_2 - y_1}{x_2 - x_1}). So (d=\frac{5 - 1}{2 - 4}=\frac{4}{-2}=-2).

Answer:

(a = 4) (b = 1) (c = 4) (d=-2)