Instantaneous Rate of Change Formula with Sample Problems

Instantaneous Rate of Change Formula :

Instantaneous function of f(a) is  equal to the lim Δx  →0   and delta y axis and divided to section for s(J mol-1)  in joule mol-1 is equal to the lim x axis  lim Δx  →0    and time taken0   t(s) in second and multiply the Angular acceleration α(rad/s2)in radians per second squared addition of height of subtraction time taken t(s) in second and area of a(m2)) in meter2 and division of height of immersed part h(cm)  in center meter .Hence the instantaneous rate of change formula can be written as

F(a)= lim Δx  →0  Δy/Δs(J mol-1) = lim Δx  →0   t(s)(rad/s2)+h(cm))-(t(s)(a(m2))/h(cm)

Where,

Δs→ section in J mol-1

T→ time taken in second

α→ Angular acceleration in radians per second squared

h→ height of the immersed part  in cm

A → area in m2

With respect to x when x=a and y=f(x)

Sample Problems

Problem 1:

Calculate the Instantaneous rate of change of the function f(x) = 4x2 + 18 at x = 6 ?

Solution :

Known Function

Y= f(x) = 4x2 + 18

F(x)=4(2x)+0

F(x)=8

Thus the instantaneous rate of change x=26

F(6)=8(6)

F=48

Problems 2:

Calculate the Instantaneous rate of change of the function f(x) = 6x3 – 2x2 + 2x + 1 at x = 3?

Solution :

Known Function

Y= f(x) = 6x3 – 2x2 + 2x + 1

f(x) = 6(3x2) – 2(2x) + 2+ 0

f(x) =18x2-4x+2

Thus the instantaneous rate of change at x=3

f(x) =18(3)2-4(3)+2

=162-12+2=152

F(x)=152

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