Equal area property for parabolas Let f ( x ) = ax 2 + bx + c be an arbitrary quadratic function and choose two points x = p and x= q . Let L 1 be the line tangent to the graph of f at the point ( p , f ( p )) and let L 2 be the line tangent to the graph at the point ( q , f ( q )). Let x = s be the vertical line through the intersection point of L 1 and L 2 . Finally, let R 1 , be the region bounded by y = f ( x ), L 1 , and the vertical line x = s , and let R 2 be the region bounded by y = f ( x ), L 2 , and the vertical line x = s . Prove that the area of R 1 equals the area of R 2 .
Equal area property for parabolas Let f ( x ) = ax 2 + bx + c be an arbitrary quadratic function and choose two points x = p and x= q . Let L 1 be the line tangent to the graph of f at the point ( p , f ( p )) and let L 2 be the line tangent to the graph at the point ( q , f ( q )). Let x = s be the vertical line through the intersection point of L 1 and L 2 . Finally, let R 1 , be the region bounded by y = f ( x ), L 1 , and the vertical line x = s , and let R 2 be the region bounded by y = f ( x ), L 2 , and the vertical line x = s . Prove that the area of R 1 equals the area of R 2 .
Solution Summary: The author explains that the area of R_1 is equal to the amount of the value of a quadratic function.
Equal area property for parabolas Let f(x) = ax2 + bx + c be an arbitrary quadratic function and choose two points x = p and x= q. Let L1 be the line tangent to the graph of f at the point (p, f(p)) and let L2 be the line tangent to the graph at the point (q, f(q)). Let x = s be the vertical line through the intersection point of L1 and L2. Finally, let R1, be the region bounded by y =f(x), L1, and the vertical line x = s, and let R2 be the region bounded by y = f(x), L2, and the vertical line x = s. Prove that the area of R1 equals the area of R2.
Only 100% sure experts solve it correct complete solutions ok
rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.