Find an equation of the tangent line to the graph of y=g(x) at x=7 if g(7)= -6 and g'(7)=4?

Answer 1

y = f(x)

let P(7,-6) be a point on the curve

we know that that the gradient of the tangent to the curve at P is 4 (g'(7) = 4 stated)

( y -b) = (dy/dx)k (x-a)..............(1)

where (dy/dx)k denotes the value of dy/dx when a is substituted for x

here we have a = 7, b = -6 and (dy/dx)k = 4

substitute these values into (1), we have

y-(-6) = 4(x-7)

y+6 = 4x -28 >>>>>>> y = 4x-34

therefore,the equation to the tangent line to the graph of y = g(x) at the point (7,-6) is y = 4x-34

Answer 2

The polymomial in any case of a 2d order to have a tangenent enable us take second order there are a variety of of varieties. we may be able to pick g(x)= ax^2+bx+c at x =7 g(x) = -6 or -6 = 49a + 14b + c g'(x) = 2ax + b so 4 = 14 a +b or b = 4- 14 a so equtation of tangent for above sort is 2ax + 4 - 14a for a random a there are more suitable than one eqution won't be able to be determined as g isn't unique

Answer 3

Since g'(7) is 4, it means that the derivative of the function g(x) at x = 7 is 4. That means, the SLOPE of the function at x = 7 is 4. It says that g(7) = -6. This means that the point (7, -6) is on the function g(x). Now you can just use the point-slope formula:

y - y1 = m(x - x1)

y + 6 = 4(x - 7)

y + 6 = 4x - 28

y = 4x - 34

Answer 4

use the slope intercept form since the slope is given: m=4
y=4x+b
we have the point 7,-6 so
-6=4*7+b
b=-6-28=-34
y=4x-34

Answer 5

I hate trigonometry... am having a flashback of teacher Dilsa explaining that,... god I hate that subject!!!!

Answer 6

uhm

Answer 7

i have no idea

Answer 8

34.


BYE.