C4 - Differentiation Watch

bigbadb1319
Badges: 0
Rep:
?
#1
Report Thread starter 12 years ago
#1
Ex. 4C
Q2. Find the equation of the tangent to the curve y=2^x + 2^(-x) at the point (2, 4.25)

I know you have to differentiate this, but what do you do after that? :confused:
0
quote
reply
yusufu
Badges: 16
Rep:
?
#2
Report 12 years ago
#2
differentiate it then find the gradient where x=2.
then find the equation of the straight line through the point (2,4.25) with the specified gradient.
0
quote
reply
Gaz031
Badges: 15
Rep:
?
#3
Report 12 years ago
#3
(Original post by bigbadb1319)
Ex. 4C
Q2. Find the equation of the tangent to the curve y=2^x + 2^(-x) at the point (2, 4.25)

I know you have to differentiate this, but what do you do after that? :confused:
The question relies on your know the derivative of a^{x} - you can derive the result by writing a^{x}=(e^{\ln a})^{x}=e^{x\ln a} then using the derivative of e^{kx} which you should know.
Find the gradient and then apply the standard equation of a line y-y_{1}=m(x-x_{1})
0
quote
reply
Dekota
Badges: 0
Rep:
?
#4
Report 12 years ago
#4
(Original post by bigbadb1319)
Find the equation of the tangent to the curve y=2^x + 2^(-x) at the point (2, 4.25)
y = 2^x + 2^(-x)
-> dy/dx = d[2^x]/dx + d[2^(-x)]/dx
............ = d[2^x]/dx + 2^(-x)ln2.d[-x]/dx
............ = 2^x.ln2 - 2^(-x).ln2
............ = 2^(-x).(4^x - 1)ln2

sub (x = 2) into dy/dx ... 2^(-2).(4² - 1)ln2 ≈ 2.6

sub (y = 4.25, x = 2, dy/dx = 2.6) into straight line equation:

-> y - 4.25 = 2.6(x - 2)
-> y = 2.6x - 0.948
quote
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Lincoln
    Mini Open Day at the Brayford Campus Undergraduate
    Wed, 19 Dec '18
  • University of East Anglia
    UEA Mini Open Day Undergraduate
    Fri, 4 Jan '19
  • Bournemouth University
    Undergraduate Mini Open Day Undergraduate
    Wed, 9 Jan '19

Were you ever put in isolation at school?

Yes (230)
27.61%
No (603)
72.39%

Watched Threads

View All