Answer:
F(4) = 97
Step-by-step explanation:
F(x)= x³+2x²+1
when x = 4
F(4)= 4³+2(4²)+1
= 4³+2(4²)+1
= 64 + 2(16) + 1
= 64 + 32 + 1
= 97
Answer:
2(x+4)
Step-by-step explanation:
Brainliest are appreciated :)
The line y = x + 3 has slope 1, so we look for points on the curve where the tangent line, whose slope is dy/dx, is equal to 1.
y² = x
Take the derivative of both sides with respect to x, assuming y = y(x) :
2y dy/dx = 1
dy/dx = 1/(2y)
Solve for y when dy/dx = 1 :
1 = 1/(2y)
2y = 1
y = 1/2
When y = 1/2, we have x = y² = (1/2)² = 1/4. However, for the given line, when y = 1/2, we have x = y - 3 = 1/2 - 3 = -5/2.
This means the line y = x + 3 is not a tangent to the curve y² = x. In fact, the line never even touches y² = x :
x = y² ⇒ y = y² + 3 ⇒ y² - y + 3 = 0
has no real solution for y.
This would be any equation whose slope isn’t -1 or 1.
If the slope was -1, the lines would be parallel because the have the same slope.
If the slope was 1, the lines would be perpendicular because 1 is the negative reciprocal of -1.
Any line with any other slope will intersect with y=-x.
Hope this helps!
