if the tangent line to y =f(x) at (2,5) passes through the point (1,-7),find f'(2)?

Question

if the tangent line to y=f(x) at (2,5)passes through the point (1,-7),find f'(2)

Answer 1

the eqn. of tangent is
y-2=(-12/-1)(x-2)
=>y-2=12x-24
=>f(x)-2=12x-24
=>f'(x)-0=12-0
=>f'(x)=12
=>f'(2)=12

therefore f'(x)=12 for an value of x

Answer 2

You just have to find the slope of the tangent line. It's a line, and we know two of its points (2,5) and (1,-7), so now it's straightforward.

(5+7)/(2-1) = 12

Therefore, f'(2)=12

Answer 3

You just have to find the slope of the tangent line. It's a line, and we know two of its points (2,5) and (1,-7), so now it's straightforward.

(5+7)/(2-1) = 12

Therefore, f'(2)=12

Answer 4

The slope of the tangent line is (5-(-7)) /(2-1)= 12

Since the slope of the tangent line at a point is equal to the derivative at that point, f'(2) = 12.

Answer 5

Any line tangent to a function has the same slope on the point of intersection. The slope of the function f(x) is given by employing its first spinoff f'(x). we are informed the tangent line intersects our function at aspect (a million,2), so f'(a million) will be equivalent to the slope of the tangent line. on the grounds that all of us understand 2 factors the line passes by potential of, we are able to locate its slope (m): f'(x) = m = (y?-y?)/(x?-x?) = (2+a million)/(a million+a million) = 3/2

Answer 6

Well, you have a line and two points on it. Surely you can find the line's slope from knowing those two points.

Answer 7

this is a trick question.. you were already given f(2) for y=f(x)

(2,5) is (x,y).. so f(2) = 5