Please Help Calculus Question. If y=3x^2 + 4x - 5 what is the slope of the line tangent to the point (3,4)?

Question

The answer says y' = 6x + 4, then substitute in x=3 and you get y'=18+4=22

I don't understand how the derivative of y is y'=6x + 4?

Answer 1

In order to do the derivative usually u lower the exponent and for the new exponent u subtract one from the original exponent ... and if you have more than one term, u just take the derivative of each term separately. for example in 3x^2 the exponent is 2 so u lower it and now u have 2*3x and the exponent of x is just one because 2-1=1. for the term 4x the exponent of x is 1 so u have 1*4 x^0 and because anything to the power or 0 is one that simplifies to just 4. The last term is a constant and the derivative of a constant is always 0. so when u combine all the derviatives u end up with 6x + 4...
Hope it helps :)

Answer 2

If y = x^a
y' = ax^(a-1) also
If y= cx
y' = c
therefore the derivative of the equation is
y' = 3(2)x^(2-1) + 4 because the serivative od a constant is 0.
y' = 6x + 4 QED

Answer 3

you minus the power of x by one and multiply the number infront of x by the original power

(2x3 = 6) (2-1 = 1) so 6x^1 = 6x
(1x4 = 4) (1-1 = 0) So 4x^0 = 4x1 = 4
So 6x + 4
and 5 is nothing because it doesnt have a power of x so it cant be derived.

Answer 4

the derivative of x^n = n x^(n-1)

so 3x^2 =? 3 * 2 * x^(2-1) = 6x
and 4x = 4 * 1 * x ^(1-1) = 4 {(x^0) = 1}

Answer 5

All of the formal definitions aside, if you can't find the derivative of the equation, f(x) = 3x^2 + 4x - 5, you're in serious need of some tutoring, or soul searching; one or the other. Or..maybe you could just study the material instead of lamenting the fact you have to take calculus in the first place....Good luck.

Answer 6

Differentiation Formula (Fact)
f (x) = a x ^ n
f `(x) = (n a) x ^ (n-1)

f (x) = 3 x ² + 4 x - 5
f `(x) = 6 x + 4
f `(3) = 18 + 4 = 22
Slope (gradient) m = 22

Answer 7

suppose y = x^n,
dy/dx = n*x^(n - 1)

And derivative of a constant is 0,

so if y = 3x^2 + 4x - 5
dy/dx = 3*2*x^(2 - 1) + 4*1*x^(1 - 1) - 0
dy/dx = 6x + 4
at x = 3
dy/dx = 22 ---> slope

Answer 8

Use chain rule to find derivitive y' = e^x / x + (ln x) e^x = [1/x + ln x] e^x Substitute x=2 into this to find y',the instant slope at the point.

Answer 9

y=3x^2 + 4x - 5
let y=Δy+y
let x=Δx+x
definition of derivative
Δy+y=3(Δx+x)^2+4(Δx+x)-5
Δy=3(Δx+x)^2+4(Δx+x)-5-(3x^2 + 4x - 5 )
Δy=3(Δx^2+2Δxx+x^2)+4Δx+4x-5-3x^2-4x+5
Δy=3Δx^2+6Δxx+3x^2+4Δx+4x-5-3x^2-4x+5
Δy=3Δx^2+6Δxx+4Δx
Δy=Δx(3Δx+6x+4)
Δy/Δx=3Δx+6x+4
lim Δx->0 Δy/Δx=lim Δx->0 3Δx+6x+4=6x+4
y'=m=6x +4
at P(3,4)
m=6(3)+4=22
find the equation of the tangent line
y-y1=m(x-x1)
y-4=22(x-3)
y-4=22x-66
y=22x-62